A367925 Expansion of e.g.f. 1/(4 - x - 3*exp(x)).
1, 4, 35, 459, 8025, 175383, 4599507, 140728437, 4920898317, 193579534155, 8461200381111, 406815231899409, 21337866382711521, 1212458502624643719, 74193773349948903483, 4864422156647044661949, 340191752483516373189621, 25278147388666498256368323
Offset: 0
Keywords
Programs
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PARI
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=i*v[i]+3*sum(j=1, i, binomial(i, j)*v[i-j+1])); v;
Formula
a(0) = 1; a(n) = n * a(n-1) + 3 * Sum_{k=1..n} binomial(n,k) * a(n-k).